Estimation of abnormal sensors

ABSTRACT

Provided is an estimation apparatus including a target data acquiring section operable to acquire target data serving as an examination target, the target data output by a plurality of sensors, a calculating section operable to calculate, for each of a plurality of sensor groups that each include two sensors among the plurality of sensors, a degree of outlierness of the target data relative to a reference data distribution of output from the sensor group, and an estimating section operable to estimate a sensor among the plurality of sensors to be a source of outlierness, based on a calculation result of the calculating section.

BACKGROUND

Technical Field

The present invention relates to estimating abnormal sensors.

Related Art

A conventional method includes mounting a plurality of sensors in acomplex system such as an automobile or manufacturing apparatus,analyzing a plurality of pieces of time sequence data acquired from theplurality of sensors, and monitoring the presence of abnormalities, asshown in Japanese Patent Application Publication No. 2010-78467, forexample.

With such a method, the amount of sensor abnormality is scored andidentified based on the amount of change in the relational structurebetween groups of sensors including a group of sensors indicatingdetection results for which an input signal is within a normal signalrange, i.e. normal sensors, and a group of sensors indicating detectionresults for which the input signal is in an abnormal signal range, i.e.abnormal sensors, from the pieces of time sequence data. However, with amethod such as described in Japanese Patent Application Publication No.2010-78467, the relational structure between the sensors has a linearrelationship, and therefore it is difficult to handle a complexnon-linear relationship that actually occurs among a plurality ofsensors. In other words, with the conventional processing method, evenwhen there is normal data corresponding to a non-linear relationshipamong the sensors, this data could be judged to be abnormal due to beingan outlier from a linear model. Furthermore, with the conventionalprocessing method, even when there is abnormal data that is an outlierfrom the non-linear relationship among the sensors, this data could bejudge to be normal if the data matches a linear model.

SUMMARY

According to a first aspect of the present invention, provided is anapparatus including a target data acquiring section operable to acquiretarget data serving as an examination target, the target data output bya plurality of sensors, a calculating section operable to calculate, foreach of a plurality of sensor groups that each include at least twosensors among the plurality of sensors, a degree of outlierness of thetarget data relative to a reference data distribution of output from thesensor group, and an estimating section operable to estimate a sensoramong the plurality of sensors to be a source of outlierness, based on acalculation result of the calculating section. The first aspect may beoperable to cause the reference data distribution to be compatible withthe relational structure among the sensors, thereby enabling thehandling of any linear or non-linear relationship among the sensors. Thefirst aspect is also provided as a method and a computer programproduct.

According to a second aspect of the present invention, provided is anapparatus in which the calculating section is further operable tocalculate, for each of the plurality of sensors, the degree ofoutlierness of each sensor group including the sensor, and theestimating section is further operable to calculate, for each sensor, adegree of association with which the sensor is associated withoutlierness, from the at least two degrees of outlierness calculated forthe groups including the sensor, and estimates whether the sensor is asource of outlierness based on the degree of association calculated foreach sensor. The second aspect may be operable to estimate the sourcesof outlierness and easily perform the estimation based on the degree ofassociation between two sensors.

According to a third aspect of the present invention, provided is anapparatus in which the estimating section is further operable toestimate each sensor having a degree of association that is greater thanor equal to a reference value relative to be a source of outlierness.The third aspect may be operable to perform the estimation operationbased on the reference value, even if the number of sensors that arecauses of outlierness are not discovered.

According to a fourth aspect of the present invention, provided is anapparatus in which the estimating section is further operable tosequentially select sensors to be sources of outlierness, in order ofdegree of association beginning with a sensor having a highest degree ofassociation. The fourth aspect may be operable to select the sensors tobe sources of outlierness in a probable order, and may be operable toattach a score of the probable order to the selected sensors.

According to a fifth aspect of the present invention, provided is anapparatus including a reference data acquiring section operable toacquire reference data serving as a reference for output of theplurality of sensors, and a distribution generating section operable togenerate, for each of the plurality of sensor groups, a reference datadistribution of output from the sensor group. The fifth aspect may beoperable to generate the reference data distribution corresponding tothe relational structure among the sensors.

According to a sixth aspect of the present invention, provided is anapparatus including a reference data acquiring section operable toacquire reference data serving as a reference for output of a pluralityof sensors, a distribution generating section operable to generate, foreach of a plurality of sensor groups that each include at least twosensors among the plurality of sensors, a reference data distribution ofoutput from the sensor group, and an output section operable to outputthe reference data distribution generated for each sensor group. Thesixth aspect may be operable to generate the reference data distributioncorresponding to the relational structure among the sensors,independently from the estimating apparatus that estimates the sensorsthat are causes of outlierness. The sixth aspect is also provided as acomputer program product.

The summary clause does not necessarily describe all features of theembodiments of the present invention. The present invention may also bea sub-combination of the features described above.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an exemplary configuration of an estimation apparatus 100along with a plurality of sensors 10, according to an embodiment of thepresent invention.

FIG. 2 shows an operational flow of an estimation apparatus, accordingto an embodiment of the present invention.

FIG. 3 shows a first example of a reference data distribution and targetdata, according to an embodiment of the present invention.

FIG. 4 shows a second example of a reference data distribution andtarget data, according to an embodiment of present invention.

FIG. 5 shows an example in which the degree of outlierness of a sensorgroup is arranged in a matrix, according to an embodiment of presentinvention.

FIG. 6 shows an example of a matrix generated by removing the data inthe column and row of the sensor estimated to be an abnormal sensor,according to an embodiment of present invention has estimated.

FIG. 7 shows another example of a matrix generated by removing the datain the column and row of the sensor estimated to be an abnormal sensor,according to an embodiment of present invention.

FIG. 8 shows an estimation apparatus 200, according to an embodiment ofpresent invention.

FIG. 9 shows an exemplary hardware configuration of a computer 1900 thatfunctions as a system, according to an embodiment of the presentinvention.

DETAILED DESCRIPTION

Hereinafter, example embodiments of the present invention will bedescribed. The example embodiments shall not limit the inventionaccording to the claims, and the combinations of the features describedin the embodiments are not necessarily essential to the invention.

FIG. 1 shows an exemplary configuration of an estimation apparatus 100along with a plurality of sensors 10, according to an embodiment of thepresent invention. The sensors 10 may be included with a target object,such as a transportation vehicle, e.g. an automobile, an airplane, aboat, etc., a manufacturing apparatus, a monitoring apparatus, etc., andmay transfer detection results to the estimation apparatus 100. Thesensors 10 may be connected to the estimation apparatus 100 throughwires, or may be connected wirelessly.

The sensors 10 may be any type of sensor, such as temperature sensors,pressure sensors, position sensors, angle sensors, location sensors,fluid level sensors, rotational speed sensors, acceleration sensors,angular speed sensors, geomagnetic sensors, flow rate sensors, oxygensensors, or the like. There can be any number of sensors 10, and in someembodiments there are more than a thousand sensors.

The estimation apparatus 100 of the present embodiment acquires theoutput of the plurality of sensors 10, which have a non-linearrelationship among one another, and estimates the accuracy of anyabnormal sensors among the plurality of sensors 10. The estimationapparatus 100 includes a reference data acquiring section 110, adistribution generating section 120, a target data acquiring section130, a storage section 140, a calculating section 150, and an estimatingsection 160.

The reference data acquiring section 110 may be operable to acquirereference data serving as a reference for output of the plurality ofsensors 10. The reference data acquiring section 110 may communicatewith the sensors 10 and acquire, as the reference data, the output ofthe sensors 10 that are operating normally. If each of the sensors 10are being operationally tested, then the reference data acquiringsection 110 may acquire the results of the operational tests as thereference data.

The distribution generating section 120 may be operable to generate, foreach of a plurality of sensor groups that are each obtained by selectinga portion of the plurality of sensors 10, a distribution of thereference data of the output from the sensor group. The distributiongenerating section 120 may communicate with the reference data acquiringsection 110, receive the reference data of the sensors 10, and generatea distribution of the reference data. The distribution generatingsection 120 may form a set of two or more sensors 10 from among theplurality of sensors 10 as a sensor group. The distribution generatingsection 120 may form a set of a prescribed number of sensors 10 as asensor group, and may generate the distribution of the reference datafor each of these sensor groups. The distribution generating section 120may generate the reference data distribution by using known distributionfunctions such as a normal distribution, a logistic distribution, aPoisson distribution, or a kernel function.

The target data acquiring section 130 may be operable to acquire targetdata for the examination target output by the plurality of sensors 10.The target data acquiring section 130 may communicate with the pluralityof sensors 10 and acquire the target data. The target data acquiringsection 130 may be connected to a network or the like, and acquire thetarget data via the network. The target data acquiring section 130 mayread and acquire the target data stored in an external storageapparatus, such as a database.

The storage section 140 may be operable to store data to be processed bythe estimation apparatus 100. The storage section 140 may communicatewith the distribution generating section 120, receive the reference datadistribution, and store the reference data distribution. The storagesection 140 may communicate with the target data acquiring section 130,receive the target data, and store the target data. The storage section140 may store each of the intermediate data, calculation results,parameters, and the like generated by (or used in) the process by whichthe estimation apparatus 100 outputs the estimation results. In responseto a request from any component in the estimation apparatus 100, thestorage section 140 may supply the stored data to the source of therequest. In response to a request by the calculating section 150, thestorage section 140 may supply the calculating section 150 with thestored reference data distribution and target data. The storage section140 may be a computer readable storage medium such as an electricstorage device, a magnetic storage device, an optical storage device, anelectromagnetic storage device, a semiconductor storage device, etc.

The calculating section 150 may be operable to generate, for each of aplurality of sensor groups obtained by selecting a portion of theplurality of sensors 10, a degree of outlierness of the target datarelative to the reference data distribution of the output from thesensor group. The calculating section 150 may communicate with thestorage section 140 and read the stored reference data distribution andtarget data. The calculating section 150 may communicate with thedistribution generating section 120 and/or the target data acquiringsection 130, and receive the reference data distribution and/or thetarget data.

The calculating section 150 may calculate the degree of outlierness ofthe target data from the reference data distribution. The calculatingsection 150 may calculate how likely it is that the target data is anoutlier. The calculating section 150 may calculate the degree ofoutlierness of the target data from the target data acquired from asensor group and the reference data distribution of this sensor group.The calculating section 150 may sequentially calculate the correspondingdegree of outlierness for each sensor group.

For each sensor group, the calculating section 150 may set the referencedata distribution as a distribution of the output in history data,calculate the occurrence rate of target data corresponding to thisoutput distribution, and calculate the degree of outlierness based onthe occurrence rate. Alternatively, the calculating section 150 maycalculate the degree of outlierness as a local outlier factor by using aknown outlier detection method.

The calculating section 150 may be operable to calculate, for each ofthe plurality of sensors 10, the degree of outlierness of each set oftwo or more sensors 10 including the sensor 10. The calculating section150 may calculate the degree of outlierness for a prescribed number ofsensors 10 corresponding to the reference data distribution generated bythe distribution generating section 120 for this prescribed number ofsensors 10, e.g. this sensor group, using the target data acquired fromthis prescribed number of sensors 10. In other words, if thedistribution generating section 120 selects sensor groups that eachinclude two sensors 10 from among the plurality of sensors 10 andgenerates the reference data distribution for these groups, then thecalculating section 150 may be operable to calculate the degree ofoutlierness for each of these sensor groups obtained by selecting twosensors 10 from among the plurality of sensors 10. The calculatingsection 150 may calculate, as the degree of outlierness of a pluralityof sensors 10, the degree of outlierness of the target data output bythe sensors 10 included in a sensor group relative to the reference datadistribution of this sensor group.

The estimating section 160 may be operable to estimate a sensor 10 to bea source of outlierness, based on the calculation results of thecalculating section 150. The estimating section 160 may communicate withthe calculating section 150 and receive the degree of outliernesscorresponding to the sensor groups. The estimating section 160 maycalculate a degree of association with which the plurality of sensors 10are related to this outlierness, based on the degrees of outliernesscorresponding to the plurality of sensor groups. In other words, theestimating section 160 may be operable to calculate a degree ofassociation with which each sensor 10 is associated with an outlierness,from two or more degrees of outlierness calculated for a set of two ormore sensors 10 including this sensor 10.

The estimating section 160 may calculate the degree of association withwhich one sensor 10 is associated with outlierness, based on a pluralityof degrees of outlierness corresponding to a plurality of sensor groupsincluding this one sensor 10. The estimating section 160 may calculate,as the degree of association with which one sensor 10 is associated withoutlierness, the sum of a plurality of degrees of outliernesscorresponding to a plurality of sensor groups that include this onesensor 10.

The estimating section 160 may be operable to estimate whether eachsensor 10 is a source of outlierness, based on the degree of associationcalculated for the sensor 10. The estimating section 160 may be operableto select sensors 10 that are sources of outlierness in order, beginningwith the sensor 10 having the highest degree of association. Theestimating section 160 may output the sensors 10 selected as sources ofoutlierness as the estimation result.

Each of the reference data acquiring section 110, distributiongenerating section 120, target data acquiring section 130, calculatingsection 150, and estimating section 160, may be a circuit, a shared ordedicated computer readable medium storing computer readable programinstructions executable by a shared or dedicated processor, etc. Thecircuits, computer-readable mediums, and/or processors may beimplemented in shared or dedicated servers.

The estimation apparatus 100 according to the present embodimentcalculates, for each set including two or more sensors 10, i.e. for eachsensor group, the degree of outlierness of the target data acquired fromthe two or more sensors 10. For each sensor 10, the estimation apparatus100 calculates the degree of association of the sensor 10 from theplurality of degrees of outlierness corresponding to sensor groupsincluding this sensor 10, and selects the sensors estimated to besources of outlierness according to these degrees of association. Anexample of the operation of this estimation apparatus 100 is describedusing FIG. 2.

FIG. 2 shows an operational flow of an estimation apparatus, accordingto an embodiment of present invention. In the present embodiment, theestimation apparatus 100 selects and outputs sensors, such as sensors10, estimated to be sources of outlierness, by performing the processfrom S210 to S250. In the example shown in FIG. 2, the estimationapparatus performs processing for a sensor group that is a set includingtwo sensors. FIG. 2 shows an exemplary operational flow of an estimationapparatus, such as the estimation apparatus 100 shown in FIG. 1, but theestimation apparatus 100 shown in FIG. 1 is not limited to thisoperational flow, and the operational flow of FIG. 2 may be performed byother apparatuses.

First, a reference data acquiring section, such as the reference dataacquiring section 110, may acquire the reference data (S210). Thereference data acquiring section may acquire, as the reference data,output occurring in a case where the plurality of sensors is operatingnormally. For example, the reference data acquiring section may acquire,as the reference data, the output occurring in a case where the targetobject on which the plurality of sensors are mounted has operated for aprescribed time. Here, if the target object is a transportation vehicle,the reference data acquiring section may acquire, as the reference data,the output during a period when the target object moves a prescribeddistance or within a prescribed range.

Next, a distribution generating section, such as the distributiongenerating section 120, may form sensor groups that each include a setof two sensors from among the plurality of sensors, and generate adistribution of the reference data for each sensor group (S220). Inother words, the distribution generating section may generate areference data distribution for the two sensors in each set of twosensors.

The distribution generating section may generate each reference datadistribution for each sensor group of two sensors in a two-dimensionalcoordinate system, where the output of one of the two sensors isexpressed on the X axis and the output of the other of the two sensorsis expressed on the Y axis. If n reference data distributions are beinggenerated for each sensor group of n sensors, the distributiongenerating section may generate the reference data distributions in ann-dimensional coordinate system, where the reference data of the nsensors is expressed in a coordinate system with n dimensions.

The distribution generating section may generate each reference datadistribution using at least one known distribution. The distributiongenerating section may generate each reference data distribution bycombining two or more known distributions. Since the relationalstructure among the plurality of sensors is a complex non-linearrelationship, the distribution generating section preferably generateseach of the reference data distributions using a distribution functionthat can handle this non-linear relationship.

The distribution generating section may generate the reference datadistribution corresponding to such a non-linear relationship by using akernel function (e.g. Gaussian kernel, Epanechnikov kernel, orRectangular kernel) that is known as a kernel density estimation.Alternatively, the distribution generating section may generate each ofthe reference data distributions using a plurality of normaldistributions. The distribution generating section may generate each ofthe reference data distributions by combining a plurality ofdistribution functions. If the processing time is to be shortened, thedistribution generating section may generate each of the reference datadistributions using one normal distribution.

The distribution generating section may generate the reference datadistributions corresponding to all of the sensor groups, i.e. allcombinations of two sensors, among the plurality of sensors. Thedistribution generating section may store the generated reference datadistributions in a storage section, such as the storage section 140.

Next, a target data acquiring section, such as the target data acquiringsection 130, may acquire the target data (S230). The target dataacquiring section may acquire, as the target data, the output of theplurality of sensors. As an example, the target data acquiring sectionmay acquire, as the target data, the output at a timing or during a timeperiod when abnormalities are to be detected during operation of thetarget object on which the plurality of sensors are mounted. Here, ifthe target object is a transportation vehicle, the target data acquiringsection may acquire, as the target data, the output during a time whenthe target object is moving.

If the output during a time when the target object moves a prescribeddistance or within a prescribed range is acquired by the reference dataacquiring section as the reference data, then the target data acquiringsection may acquire, as the target data, the output of the target objectduring a time when the target object again moves the prescribed distanceor in the prescribed range. In other words, the estimation apparatus mayacquire in advance the reference data during a first period when thetarget object moves a prescribed amount, acquire the target data duringa second period when the target object again moves the prescribedamount, and detect whether an abnormality has occurred during the secondperiod based on the reference data and the target data.

Next, for each sensor group, a calculating section, such as thecalculating section 150, may calculate the degree of outlierness betweenthe target data of the two sensors of the sensor group and the referencedata distribution corresponding to the sensor group (S240). If thedistribution generating section generates the reference datadistribution as two-dimensional coordinates based on the two sensors,then the calculating section may calculate the degree of outliernessbetween the target data of these two sensors and this reference datadistribution.

If the distribution generating section generates the reference datadistribution using a kernel function, then the calculating section maycalculate the degree of outlierness of the target data as the occurrencerate of this data. The occurrence rate can be calculated as the kerneldensity estimation using a known calculation method. The calculatingsection may use the logarithm of the occurrence rate, in order toenlarge the range of the numbers being handled. Furthermore, thecalculating section may multiply the occurrence rate by a negativecoefficient, e.g. −1, such that the value becomes larger when the degreeof outlierness is larger. In other words, the calculating section maycalculate the negative log-likelihood as the degree of outlierness.

In this way, the calculating section may calculate the correspondingdegree of outlierness for each sensor group. In other words, thecalculating section may calculate the corresponding degree ofoutlierness for each set of two sensors. The calculating section maycalculate the degree of outlierness for all of the sensor groups amongthe plurality of sensors. Here, with i representing the number of thefirst sensor included in a sensor group and j representing the number ofthe second sensor, the degree of outlierness can be represented asΓ_(ij) (i≠j).

With d representing the number of sensors, the calculating section maycalculate Γ_(ij) as the combination of all the numbers of i and j from 1to d (Γ_(ij)=Γ_(ji),). In this case, the calculating section arrangesΓ_(ij) in a matrix with i rows and j columns, and calculates the valueof Γ_(ij) excluding the diagonal matrix (i=j).

Next, an estimating section, such as the estimating section 160, mayestimate the sensors that are sources of outlierness based on the degreeof outlierness Γ_(ij) of the sensor groups (S250). The estimatingsection may estimate the sources of outlierness, e.g. the abnormalsensors, to be sensors that are included more often in sensor groupshaving a large value for the degree of outlierness Γ_(ij). If the numberof abnormal sensors is determined to be k, then the estimating sectioncan obtain an estimation result of J={1, 2, . . . , k} for themathematical set of abnormal sensors, by solving the combinatorialoptimization problem for the following two expressions.Ĵ={1,2, . . . ,d}\Î  Expression 1:Î=argmin_(I⊂{1,2, . . . ,d})Σ_(i,j∈I)Γ_(ij) ,s.t.|I|=d−k  Expression 2:

Here, the estimation value of J has a “^” symbol appended thereto and isreferred to as “J hat” on the left side of Expression 1. Furthermore,the mathematical set of sensors with a small degree of outlierness, i.e.normal sensors, is represented as I={1, 2, . . . , d-k}, and theestimated value of I has a “^” symbol appended thereto and is referredto as “I hat.” Furthermore, the symbol “\” represents the mathematicalset difference. In other words, Expression 1 expresses the estimatedvalue of the abnormal sensors as the mathematical set obtained bysubtracting the estimated value of the normal sensors from themathematical set {1, 2, . . . , d} of the sensors, i.e. thecomplementary mathematical set of sensors with a small degree ofoutlierness.

Furthermore, argmin f(x) represents x in a case where f(x) is at aminimum, and Expression 2 means that the mathematical set I in a casewhere the right side of the expression, i.e. the total of the degree ofoutlierness Γ_(ij) for i and j, is at a minimum is the estimated valuefor I. The number of terms in the mathematical set I is set to d-k asthe constraint condition (s. t.).

The combinatorial optimization problem of Expression 1 and Expression 2can be solved by known algorithms, software, or the like if the numberof sensors d is approximately several hundred or less. Furthermore, evenif the number of sensors d does exceed several hundred, it is possibleto efficiently obtain an approximation solution using a known algorithm,such as a greedy algorithm, as described further below. Accordingly, theestimating section can accurately estimate the mathematical set ofabnormal sensors.

If the number of abnormal sensors k is not determined, then theestimating section may estimate each mathematical set of abnormalsensors for a plurality of values of k. In this case, a user of theestimation apparatus may select a plausible estimation result based onthe plurality of estimation results of the estimating section.Alternatively, the estimating section may estimate the mathematical setof abnormal sensors by combining a threshold value, setting value, orthe like with a known algorithm such as the greedy algorithm describedfurther below.

In the manner described above, the estimation apparatus of the presentembodiment can estimate the abnormal sensors based on the degree ofoutlierness between the reference data distributions of the sensorgroups and the target data of the sensor groups. The estimationapparatus generates the reference data distributions of the sensorgroups according to a complex non-linear relationship among the sensors,and therefore can perform an estimation in accordance with the actualoperation of the plurality of sensors. If it is assumed that therelational structure among the sensors is linear, then such a case wouldcorrespond to the reference data distributions of the sensor groupshaving a linear relationship. Accordingly, in cases where thedistribution generating section according to the present embodimentgenerates the reference data distributions of the sensor as one normaldistribution, the estimating section can perform the estimation moreaccurately than in cases where it is assumed that the relationalstructure among the sensors is linear.

FIG. 3 shows a first example of a reference data distribution and targetdata, according to an embodiment of present invention. FIG. 3 shows anexample in which a distribution generating section, such as thedistribution generating section 120, expresses the reference data andthe target data as two-dimensional coordinates, where output of one ofthe two sensors included in the sensor group is represented on the Xaxis and the output of the other sensor is represented on the Y axis. Inother words, in FIG. 3, the horizontal axis (X axis) represents the dataof a first sensor and the vertical axis (Y axis) represents the data ofa second sensor. In the example of FIG. 3, the data indicated by a “+”symbol represents reference data for the sensor group of the firstsensor and the second sensor, and data represented by a circular symbolrepresents the target data for the sensor group of the first sensor andthe second sensor.

The distribution generating section may generate the reference datadistribution based on the reference data of this sensor group. In otherwords, the distribution generating section may generate, as thereference data distribution, a distribution function in which thecoordinate regions where more reference data is detected have largervalues.

A calculating section, such as the calculating section 150, maycalculate the degree of outlierness of the target data from thisreference data distribution. In the example of FIG. 3, the target datais detected within a range over which the reference data is distributed,and therefore the calculating section may calculate the degree ofoutlierness to be a smaller value. In other words, the target data ofthe sensor group, i.e. the first sensor and the second sensor, is withina range of the distribution of the reference data acquired from thesensor group when operating normally, and therefore this sensor groupcan be estimated to be operating normally.

FIG. 4 shows a second example of a reference data distribution andtarget data, according to an embodiment of present invention. In thesame manner as in FIG. 3, FIG. 4 shows an example in which the referencedata and the target data are expressed as two-dimensional coordinates,where output of one of the two sensors included in the sensor group isrepresented on the X axis and the output of the other sensor isrepresented on the Y axis. In other words, in FIG. 4, the horizontalaxis (X axis) represents the data of a first sensor and the verticalaxis (Y axis) represents the data of a third sensor. In the example ofFIG. 4, the data indicated by a “+” symbol represents reference data forthe sensor group of the first sensor and the third sensor, and datarepresented by a circular symbol represents the target data for thesensor group of the first sensor and the third sensor.

A distribution generating section, such as the distribution generatingsection 120, may generate the reference data distribution based on thereference data of this sensor group. In other words, the distributiongenerating section may generate, as the reference data distribution, adistribution function in which coordinate regions where more referencedata is detected have larger values.

A calculating section, such as the calculating section 150, maycalculate the degree of outlierness of the target data from thisreference data distribution. In the example of FIG. 4, the target datais detected outside of the range in which the reference data isdistributed, and therefore the calculating section may calculate thedegree of outlierness to be larger than the value of the degree ofoutlierness calculated for the example of FIG. 3. In other words, thetarget data of the sensor group, i.e. the first sensor and the thirdsensor, is outside of the range of the reference data distributionacquired from the sensor group when operating normally, and therefore atleast one sensor of the sensor group can be estimated as possiblyoperating abnormally.

In the manner described above, the distribution generating section ofthe present embodiment generates a reference data distribution thatreflects the non-linear relational structure among the sensors, and thecalculating section calculates the degree of outlierness of the targetdata from this reference data distribution. Therefore, it is possible tocalculate the degree of outlierness for each sensor group whilereflecting the non-linear relational structure among the sensors. Anestimation apparatus, such as the estimation apparatus 100, cancalculate the degree of outlierness Γ_(ij)for all of the sensor groupsby acquiring the reference data and target data from each of thesensors.

FIG. 5 shows an example in which the degree of outlierness Γ_(ij) of asensor group is arranged in a matrix with i rows and j columns,according to an embodiment of present invention. FIG. 5 shows an examplein which the degrees of outlierness Γ_(ij) of 32 sensors are representedby the shading amount in a pattern of squares in i rows and j columns.In FIG. 5, all of the squares in the sixth column (sixth row) are shownwith a darker pattern than the other squares, and this indicates anexample in which the degree of outlierness Γ_(6j) (Γ_(i6)) is a largervalue than the other degrees of outlierness. In other words, among theplurality of sensor groups, the degrees of outlierness of the sensorgroups that include the sixth sensor exhibit a larger value than thedegrees of outlierness of the other sensor groups. Therefore, it can beestimated that the sixth sensor is an abnormal sensor.

As shown in FIG. 5, an estimating section, such as the estimatingsection 160, has arranged the degree of outlierness Γ_(ij) in a matrix,and may use a known estimation method of a greedy algorithm to estimatewhether a sensor is an abnormal sensor. The estimating section maycalculate, as each degree of association, the sum Σ_(j)Γ_(ij) of thedegree of outlierness Γ_(ij) for each column of a matrix such as shownin FIG. 5. Alternatively or in addition, the estimating section maycalculate, as each degree of association, the sum Σ_(i)Γ_(ij) of thedegree of outlierness Γ_(ij) for each row of a matrix such as shown inFIG. 5.

The estimating section may select sensors that are sources ofoutlierness in order, beginning with the sensor having the highestdegree of association. In other words, the estimating section may selectthe abnormal sensors in order beginning from a j-th sensor having thehighest value for Σ_(j)Γ_(ij), as the estimation result. Specifically,in the example of FIG. 5, the estimating section may estimate the sixthsensor to be an abnormal sensor, according to the sum Σ₆Γ_(ij) of thedegree of outlierness of the sixth column having the largest value. Theestimating section may then reduce the size of the matrix by removingthe data in the sixth column and sixth row indicating the degree ofoutlierness of the sixth sensor, and perform an estimation of the nextabnormal sensor.

FIG. 6 shows an example of a matrix generated by removing the data inthe column and row of the sensor estimated to be an abnormal sensor,according to an embodiment of present invention. An estimating section,such as the estimating section 160, may be operable to calculate thedegree of association with which each sensor is associated withoutlierness, from the degree of outlierness calculated for sets ofsensors (sensor groups) that do not include the sensors already selectedas sensors that are sources of outlierness. The estimating section mayperform a subsequent estimation from the matrix shown in FIG. 6 having31 columns and 31 rows, which is obtained by removing the target data ofthe sensor groups including the sixth sensor.

Specifically, in the example of FIG. 6, the estimating section mayestimate the seventh sensor to be an abnormal sensor, according to thesum Σ₆Γ_(ij) of the degree of outlierness of the sixth column having thelargest value. The estimating section may then reduce the size of thematrix by removing the data in the sixth column and sixth row indicatingthe degree of outlierness of the seventh sensor, and perform anestimation of the next abnormal sensor. Here, if the abnormal sensorsare being estimated in order beginning with the sensor having thehighest degree of association, then the estimating section may attach ascore to each of the estimated abnormal sensors. The estimating sectionmay attach a maximum score to the sixth sensor that is estimated first,and may attach a second-highest score to the seventh sensor that isdetected next. The estimating section may use the value of the degree ofassociation as the score.

FIG. 7 shows another example of a matrix generated by removing the datain the column and row of the sensor estimated to be an abnormal sensor,according to an embodiment of present invention. The estimating sectionmay perform the subsequent estimation from the matrix shown in FIG. 7having 30 columns and 30 rows, which is obtained by removing the targetdata of the sensor groups including any one of the sixth sensor and theseventh sensor. If a number k of abnormal sensors is to be discovered,an estimating section, such as the estimating section 160, may repeatthe estimation described above k times to sequentially estimate kabnormal sensors. In other words, the estimating section is operable toselect a set number (or a predetermined number) of sensors as sensorsthat are sources of outlierness, in order beginning with a sensor havingthe highest degree of association.

If a number k of abnormal sensors is not to be discovered, then theestimating section may determine whether to repeat the estimation of theabnormal sensors. In other words, the estimating section may be operableto determine whether to further select a sensor that is a source ofoutlierness based on a total or an average of the degrees of outliernesscalculated for the sets of sensors that do not include the sensorsselected as sources of outlierness.

As an example, the estimating section may be operable to estimate thatone sensor is a source of outlierness if the one sensor has a degree ofassociation indicating an association that is greater than or equal to areference value relative to the outlierness. Specifically, theestimating section may estimate that one sensor is an abnormal sensor ifthe degree of association of the one sensor is greater than a thresholdvalue, reference value, or setting value, and then perform the nextestimation. Furthermore, the estimating section may estimate that onesensor is not an abnormal sensor if the degree of association of the onesensor is less than a threshold value, reference value, or settingvalue, and then stop the estimation operation.

Alternatively, the estimating section may be operable to estimate that asensor that has yet to be selected is a sensor that is not a source ofoutlierness if the degree of association of a most recently selectedsensor differs from the next highest degree of association by an amountgreater than or equal to a reference difference. Specifically, if thedifference between the degree of association of one sensor and thedegree of association of a sensor estimated as an abnormal sensorimmediately prior thereto is less than a threshold value, referencevalue, or setting value, then the estimating section may estimate thatthis one sensor is also an abnormal sensor, and perform the nextestimation. Furthermore, if the difference between the degree ofassociation of one sensor and the degree of association of a sensorestimated as an abnormal sensor immediately prior thereto is greaterthan a threshold value, reference value, or setting value, then theestimating section may estimate that this one sensor is not an abnormalsensor, and stop the estimation operation.

If the sum of the degrees of association of the remaining sensors thathave not yet been selected after one sensor has been selected andestimated as an abnormal sensor is less than a threshold value,reference value, or setting value, then the estimating section mayestimate that these remaining sensors are not abnormal sensors, and stopthe estimation operation. Furthermore, if the sum of the degrees ofassociation of these remaining sensors is calculated in response to therepetition of the estimation operation, and the calculation result hasdecreased from the previous reference result by an amount greater than areference value, then the estimating section may estimate that theseremaining sensors are not abnormal sensors, and stop the estimationprocess.

In the manner described above, the estimating section of the presentembodiment can output the sensors estimated to be abnormal sensors inorder, by using a greedy algorithm. Furthermore, even when a number k ofabnormal sensors is not to be discovered, the estimating section canperform an estimation of the abnormal sensors by using a threshold valueor the like or by comparing the degrees of association. Alternatively,the estimating section can output a prescribed number of abnormalsensors, by repeating the estimation a set number of times or apredetermined number of times. The estimating section may estimate thesensors in order beginning with the sensor having the highest degree ofassociation, and in this case can output the abnormal sensors in theprobable order in which these sensors are estimated as abnormal.Furthermore, the estimating section can attach a score corresponding tothe degree of association to the sensors estimated to be abnormalsensors and output these sensors.

Alternatively, the estimating section may estimate the sensors in orderbeginning with the sensor having the lowest degree of association. Inother words, the estimating section may be operable to select sensorsthat are not sources of outlierness in order, beginning with the sensorhaving the lowest degree of association. In this case, the estimatingsection may be operable to estimate that one sensor is not a source ofoutlierness if the one sensor has a degree of association indicating anassociation that is less than a reference. Specifically, if one sensorhas a degree of association that is less than a threshold value, areference value, or a setting value, then the estimating section mayestimate that this one sensor is a normal sensor.

The estimating section may be operable to calculate the degree ofassociation with which each sensor is related to outlierness from thedegree of outlierness calculated for the sets of sensors that do notinclude sensors already selected as sensors that are not sources ofoutlierness. The estimating section may perform subsequent estimationswhile decreasing the size of the matrix. If one sensor has a degree ofassociation that is greater than a threshold value, a reference value,or a setting value, then the estimating section may estimate that thisone sensor is an abnormal sensor. In this case, the estimating sectionmay then perform the next estimation, or instead of this, if theremaining sensors have a degree of association higher than that of thesensor that has just been estimated as an abnormal sensor, theestimating section may estimate that all of these remaining sensors areabnormal sensors, and then end the estimation operation.

The estimating section may be operable to estimate that sensors thathave not yet been selected are sensors that are sources of outlierness,if a difference between the degree of association of the sensor selectedmost recently and the next lowest degree of association is greater thanor equal to a reference difference. Specifically, if the degree ofassociation of one sensor is greater than the degree of association ofthe sensor estimated immediately prior by a threshold value, a referencevalue, or a setting value, then the estimating section may estimate thatthis one sensor is an abnormal sensor. If the degree of association ofone sensor is less than the degree of association of the sensorestimated immediately prior by a threshold value, a reference value, ora setting value, then the estimating section may estimate that this onesensor is not an abnormal sensor and perform the next estimation.

The estimating section may repeat the estimation until there are no moresensors remaining after removal of the already estimated sensors amongthe plurality of sensors. Alternatively, the estimating section may beoperable to select a set number of sensors or a predetermined number ofsensors as sensors that are not sources of outlierness, in orderbeginning with the sensor having the lowest degree of association. Inthis way, the estimating section 160 can output the sensors 10 in orderbeginning with the sensors determined to be operating normally, by usinga greedy algorithm.

In some embodiments, the estimation apparatus may acquire reference dataand generates a reference data distribution. In other embodiments, anestimation apparatus may use a reference data distribution generated byan external apparatus, such as the estimation apparatus described inFIG. 8. In this case, the estimation apparatus may request the referencedata distribution to the external apparatus.

FIG. 8 shows an estimation apparatus 200, according to an embodiment ofpresent invention. The estimation apparatus 200 includes an acquiringsection 230, a storage section 240, a calculating section 250, and anestimating section 260. The storage section 240, the calculating section250, and the estimating section 260 may perform substantially the sameoperations as the storage section 140, the calculating section 150, andthe estimating section 160 of the estimation apparatus 100 according toFIG. 1, except as otherwise indicated. Each of the acquiring section230, calculating section 250, and estimating section 260, may be acircuit, a shared or dedicated computer readable medium storing computerreadable program instructions executable by a shared or dedicatedprocessor, etc. The storage section 240 may be a computer readablestorage medium such as an electric storage device, a magnetic storagedevice, an optical storage device, an electromagnetic storage device, asemiconductor storage device, etc. The description of sensors 10 of isthe same as in FIG. 1, except as otherwise indicated.

The acquiring section 230 may be operable to acquire target data servingas the examination target output by the plurality of sensors 10. Theacquiring section 230 may communicate with the plurality of sensors 10and acquire the target data. The acquiring section 230 may be operableto acquire a reference data distribution. The acquiring section 230 mayacquire a reference data distribution generated by another apparatus,for example. Specifically, the acquiring section 230 may communicatewith another apparatus and acquire the reference data distribution. Theacquiring section 230 may supply the storage section 240 with theacquired target data and reference data distribution. Instead, theacquiring section 230 may supply the calculating section 250 with theacquired target data and reference data distribution.

In this way, the calculating section 250 may be operable to calculatethe degree of outlierness of the target data relative to the referencedata distribution. The estimating section 260 may be operable toestimate sensors 10 that are sources of outlierness, based on thecalculation results of the calculating section 250. Specifically, theestimation apparatus 200 of the present embodiment can estimate a sensor10 among the plurality of sensors 10 to be a source of outlierness byacquiring the reference data distribution generated by an externalapparatus, for example, and the target data of the plurality of sensors10. The external apparatus may be a generation apparatus 300 accordingto the present embodiment.

The generation apparatus 300 according to the present embodimentacquires the reference data of the plurality of sensors 10 and generatesthe reference data distribution. The generation apparatus 300 includes areference data acquiring section 310, a distribution generating section320, and an output section 340. Each of the reference data acquiringsection 310, distribution generating section 320, and output section340, may be a circuit, a shared or dedicated computer readable mediumstoring computer readable program instructions executable by a shared ordedicated processor, etc. The storage section 330 may be a computerreadable storage medium such as an electric storage device, a magneticstorage device, an optical storage device, an electromagnetic storagedevice, a semiconductor storage device, etc.

The reference data acquiring section 310 may be operable to acquirereference data that is a reference for output of the plurality ofsensors 10. The reference data acquiring section 310 may communicatewith the plurality of sensors 10 and acquire, as the reference data, theoutput of the plurality of sensors 10 when operating normally. Thereference data acquiring section 310 may operate in substantially thesame manner as the reference data acquiring section 110 of theestimation apparatus 100 in FIG. 1, except as otherwise indicated.

The distribution generating section 320 may be operable to generate, foreach of a plurality of sensor groups that are each obtained by selectinga portion of the plurality of sensors 10, a reference data distributionof the output from the sensor group. The distribution generating section320 may communicate with the reference data acquiring section 310,receive the reference data of the plurality of sensors 10, and generatethe reference data distribution. The distribution generating section 320may be operable to generate, for each of a plurality of sensor groupsthat are each obtained by selecting two sensors 10 from among theplurality of sensors 10, a reference data distribution of the outputfrom the sensor group. The distribution generating section 320 mayoperate in substantially the same manner as the distribution generatingsection 120 of the estimation apparatus 100 in FIG. 1, except asotherwise indicated.

The storage section 330 may be operable to store data to be processed bythe generation apparatus 300. The storage section 330 may communicatewith the distribution generating section 320, receive the reference datadistribution, and store the reference data distribution.

The output section 340 may be operable to output a reference datadistribution generated for each of the plurality of sensor groups, to beused by the estimation apparatus 200 to estimate sensors 10 that aresources of outlierness by calculating the degree of outlierness of thetarget data serving as the examination target output from the pluralityof sensors 10. The output section 340 may communicate with the acquiringsection 230 of the estimation apparatus 200 and supply the acquiringsection 230 with the reference data distribution. The output section 340may supply the acquiring section 230 with the reference datadistribution via a network or the like.

The generation apparatus 300 of the present embodiment described abovemay generate the reference data distribution to be used by theestimation apparatus 200 to identify the sensors 10 that are sources ofoutlierness. In this way, the generation apparatus 300 can generate thereference data distribution corresponding to the complex relationalstructure among the sensors 10, independently from the estimationapparatus 200. Accordingly, the generation apparatus 300 may generate amore accurate reference data distribution by using a processingapparatus with greater processing capability, for example. In this way,the estimation apparatus 200 can perform the estimation of abnormalsensors using a processing apparatus that is more compact than thegeneration apparatus 300, for example. Accordingly, the estimationapparatus 200 may be implemented more easily in the apparatus on whichthe plurality of sensors 10 are mounted, for example, and can performthe estimation of abnormal sensors in real time.

FIG. 9 shows an exemplary configuration of a computer 1900 according toan embodiment of the invention. The computer 1900 according to thepresent embodiment includes a CPU 2000, a RAM 2020, a graphicscontroller 2075, and a display apparatus 2080 which are mutuallyconnected by a host controller 2082. The computer 1900 also includesinput/output units such as a communication interface 2030, a hard diskdrive 2040, and a DVD-ROM drive 2060 which are connected to the hostcontroller 2082 via an input/output controller 2084. The computer alsoincludes legacy input/output units such as a ROM 2010 and a keyboard2050 which are connected to the input/output controller 2084 through aninput/output chip 2070.

The host controller 2082 connects the RAM 2020 with the CPU 2000 and thegraphics controller 2075 which access the RAM 2020 at a high transferrate. The CPU 2000 operates according to programs stored in the ROM 2010and the RAM 2020, thereby controlling each unit. The graphics controller2075 obtains image data generated by the CPU 2000 on a frame buffer orthe like provided in the RAM 2020, and causes the image data to bedisplayed on the display apparatus 2080. Alternatively, the graphicscontroller 2075 may contain therein a frame buffer or the like forstoring image data generated by the CPU 2000.

The input/output controller 2084 connects the host controller 2082 withthe communication interface 2030, the hard disk drive 2040, and theDVD-ROM drive 2060, which are relatively high-speed input/output units.The communication interface 2030 communicates with other electronicdevices via a network. The hard disk drive 2040 stores programs and dataused by the CPU 2000 within the computer 1900. The DVD-ROM drive 2060reads the programs or the data from the DVD-ROM 2095, and provides thehard disk drive 2040 with the programs or the data via the RAM 2020.

The ROM 2010 and the keyboard 2050 and the input/output chip 2070, whichare relatively low-speed input/output units, are connected to theinput/output controller 2084. The ROM 2010 stores therein a boot programor the like executed by the computer 1900 at the time of activation, aprogram depending on the hardware of the computer 1900. The keyboard2050 inputs text data or commands from a user, and may provide the harddisk drive 2040 with the text data or the commands via the RAM 2020. Theinput/output chip 2070 connects a keyboard 2050 to an input/outputcontroller 2084, and may connect various input/output units via aparallel port, a serial port, a keyboard port, a mouse port, and thelike to the input/output controller 2084.

A program to be stored on the hard disk drive 2040 via the RAM 2020 isprovided by a recording medium as the DVD-ROM 2095, and an IC card. Theprogram is read from the recording medium, installed into the hard diskdrive 2040 within the computer 1900 via the RAM 2020, and executed inthe CPU 2000.

A program that is installed in the computer 1900 and causes the computer1900 to function as an estimation apparatus, such as estimationapparatus 100 of FIG. 1, includes a reference data acquiring section, adistribution generating section, a target data acquiring section, astorage section, a calculating section, an estimating section, anacquiring section, and an output section. The program or module acts onthe CPU 2000, to cause the computer 1900 to function as a reference dataacquiring section, a distribution generating section, a target dataacquiring section, a storage section, a calculating section, anestimating section, an acquiring section, and an output section, such asthe reference data acquiring section 110, the distribution generatingsection 120, the target data acquiring section 130, the storage section140, the calculating section 150, the estimating section 160, theacquiring section 230, the storage section 240, the calculating section250, the estimating section 260, the reference data acquiring section310, the distribution generating section 320, the storage section 330,and the output section 340 described above.

The information processing described in these programs is read into thecomputer 1900, to function as a reference data acquiring section, adistribution generating section, a target data acquiring section, astorage section, a calculating section, an estimating section, anacquiring section, and an output section, which are the result ofcooperation between the program or module and the above-mentionedvarious types of hardware resources. Moreover, the estimation apparatusis constituted by realizing the operation or processing of informationin accordance with the usage of the computer 1900.

For example when communication is performed between the computer 1900and an external device, the CPU 2000 may execute a communication programloaded onto the RAM 2020, to instruct communication processing to acommunication interface 2030, based on the processing described in thecommunication program. The communication interface 2030, under controlof the CPU 2000, reads the transmission data stored on the transmissionbuffering region provided in the recording medium, such as a RAM 2020, ahard disk drive 2040, or a DVD-ROM 2095, and transmits the readtransmission data to a network, or writes reception data received from anetwork to a reception buffering region or the like provided on therecording medium. In this way, the communication interface 2030 mayexchange transmission/reception data with the recording medium by a DMA(direct memory access) method, or by a configuration that the CPU 2000reads the data from the recording medium or the communication interface2030 of a transfer destination, to write the data into the communicationinterface 2030 or the recording medium of the transfer destination, soas to transfer the transmission/reception data.

In addition, the CPU 2000 may cause all or a necessary portion of thefile of the database to be read into the RAM 2020 such as by DMAtransfer, the file or the database having been stored in an externalrecording medium such as the hard disk drive 2040, the DVD-ROM drive2060 (DVD-ROM 2095) to perform various types of processing onto the dataon the RAM 2020. The CPU 2000 may then write back the processed data tothe external recording medium by means of a DMA transfer method or thelike. In such processing, the RAM 2020 can be considered to temporarilystore the contents of the external recording medium, and so the RAM2020, the external recording apparatus, and the like are collectivelyreferred to as a memory, a storage section, a recording medium, acomputer readable medium, etc. Various types of information, such asvarious types of programs, data, tables, and databases, may be stored inthe recording apparatus, to undergo information processing. Note thatthe CPU 2000 may also use a part of the RAM 2020 to performreading/writing thereto on the cache memory. In such an embodiment, thecache is considered to be contained in the RAM 2020, the memory, and/orthe recording medium unless noted otherwise, since the cache memoryperforms part of the function of the RAM 2020.

The CPU 2000 may perform various types of processing, onto the data readfrom the RAM 2020, which includes various types of operations,processing of information, condition judging, search/replace ofinformation, etc., as described in the present embodiment and designatedby an instruction sequence of programs, and writes the result back tothe RAM 2020. For example, when performing condition judging, the CPU2000 may judge whether each type of variable shown in the presentembodiment is larger, smaller, no smaller than, no greater than, orequal to the other variable or constant, and when the condition judgingresults in the affirmative (or in the negative), the process branches toa different instruction sequence, or calls a sub routine.

In addition, the CPU 2000 may search for information in a file, adatabase, etc., in the recording medium. For example, when a pluralityof entries, each having an attribute value of a first attribute isassociated with an attribute value of a second attribute, are stored ina recording apparatus, the CPU 2000 may search for an entry matching thecondition whose attribute value of the first attribute is designated,from among the plurality of entries stored in the recording medium, andreads the attribute value of the second attribute stored in the entry,thereby obtaining the attribute value of the second attribute associatedwith the first attribute satisfying the predetermined condition.

The above-explained program or module may be stored in an externalrecording medium. Exemplary recording mediums include a DVD-ROM 2095, aswell as an optical recording medium such as a Blu-ray Disk or a CD, amagneto-optic recording medium such as a MO, a tape medium, and asemiconductor memory such as an IC card. In addition, a recording mediumsuch as a hard disk or a RAM provided in a server system connected to adedicated communication network or the Internet can be used as arecording medium, thereby providing the program to the computer 1900 viathe network.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to individualize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the embodiments of the present invention have been described, thetechnical scope of the invention is not limited to the above describedembodiments. It is apparent to persons skilled in the art that variousalterations and improvements can be added to the above-describedembodiments. It is also apparent from the scope of the claims that theembodiments added with such alterations or improvements can be includedin the technical scope of the invention.

The operations, procedures, steps, and stages of each process performedby an apparatus, system, program, and method shown in the claims,embodiments, or diagrams can be performed in any order as long as theorder is not indicated by “prior to,” “before,” or the like and as longas the output from a previous process is not used in a later process.Even if the process flow is described using phrases such as “first” or“next” in the claims, embodiments, or diagrams, it does not necessarilymean that the process must be performed in this order.

What is claimed is:
 1. An apparatus comprising: a target data acquiringsection operable to acquire target data serving as an examinationtarget, the target data output by a plurality of sensors; a calculatingsection operable to calculate, for each of a plurality of sensor groupsthat each include at least two sensors among the plurality of sensors, adegree of outlierness of the target data relative to a reference datadistribution of output from the sensor group; and an estimating sectionoperable to estimate at least one sensor among the plurality of sensorsto be a source of outlierness, based on a comparison of the degrees ofoutlierness of the sensor groups that include the at least one sensor tothe degrees of outlierness of the sensor groups that lack the at leastone sensor.
 2. The apparatus according to claim 1, wherein thecalculating section is further operable to calculate, for each of theplurality of sensors, the degree of outlierness of each sensor groupincluding the sensor, and the estimating section is further operable tocalculate, for each sensor, a degree of association with which thesensor is associated with outlierness, from the at least two degrees ofoutlierness calculated for the groups including the sensor, andestimates whether the sensor is a source of outlierness based on thedegree of association calculated for each sensor.
 3. The apparatusaccording to claim 2, wherein the estimating section is further operableto estimate each sensor having a degree of association that is greaterthan or equal to a reference value relative to be a source ofoutlierness.
 4. The apparatus according to claim 2, wherein theestimating section is further operable to sequentially select sensors tobe sources of outlierness, in order of degree of association beginningwith a sensor having a highest degree of association.
 5. The apparatusaccording to claim 4, wherein the estimating section is further operableto estimate that sensors that have not yet been selected are not sensorsthat are sources of outlierness, if a difference between the degree ofassociation of a most recently selected sensor and a next highest degreeof association is greater than or equal to a reference difference. 6.The apparatus according to claim 4, wherein the estimating section isfurther operable to sequentially select a set number of sensors to besources of outlierness.
 7. The apparatus according to claim 4, whereinthe estimating section is further operable to calculate, for each sensorthat has not been selected, the degree of association from the degreesof outlierness calculated for sensor groups that do not include sensorsthat have already been selected.
 8. The apparatus according to claim 4,wherein the estimating section is further operable to determine whetherto further select a sensor, based on a total or an average of thedegrees of outlierness calculated for sensor groups that do not includesensors that have already been selected.
 9. The apparatus according toclaim 2, wherein the estimating section is further operable to estimatethat each sensor having a degree of association less than a referencevalue is not a source of outlierness.
 10. The apparatus according toclaim 2, wherein the estimating section is further operable tosequentially select sensors not to be sources of outlierness, in orderof degree of association beginning with a sensor having the lowestdegree of association.
 11. The apparatus according claim 10, wherein theestimating section is further operable to estimate that sensors thathave not yet been selected are sensors that are sources of outlierness,if a difference between the degree of association of the most recentlyselected sensor and a next lowest degree of association of is greaterthan or equal to a reference difference.
 12. The apparatus according toclaim 9, wherein the estimating section is further operable tosequentially select a set number of sensors not to be sources ofoutlierness, in order of degree of association beginning with a sensorhaving a lowest degree of association.
 13. The apparatus according toclaim 10, wherein the estimating section is further operable tocalculate, for each sensor that has not been selected, the degree ofassociation from the degrees of outlierness calculated for sensor groupsthat do not include sensors that have already been selected.
 14. Theapparatus according to claim 1, further comprising: a reference dataacquiring section operable to acquire reference data serving as areference for output of the plurality of sensors; and a distributiongenerating section operable to generate, for each of the plurality ofsensor groups, the reference data distribution of output from the sensorgroup based on the reference data.
 15. The apparatus according to claim1, wherein the calculating section is further operable to calculate thedegree of outlierness for each sensor group.
 16. An apparatuscomprising: a reference data acquiring section operable to acquirereference data serving as a reference for output of a plurality ofsensors; a distribution generating section operable to generate, foreach of a plurality of sensor groups that each include at least twosensors among the plurality of sensors, a reference data distribution ofoutput from the sensor group based on the reference data; and an outputsection that operable to output the reference data distributiongenerated for each of the sensor groups, to be used by an apparatus thatcalculates, for each of the plurality of sensor groups, a degree ofoutlierness of target data serving as an examination target output fromthe plurality of sensors relative to the reference data distribution,and estimates at least one sensor among the plurality of sensors to be asource of outlierness, based on a comparison of the degrees ofoutlierness of the sensor groups that include the at least one sensor tothe degrees of outlierness of the sensor groups that lack the at leastone sensor.
 17. The apparatus according to claim 16, wherein thedistribution generating section is further operable to generate, foreach of the plurality of sensor groups that are each formed by selectingtwo sensors from among the plurality of sensors, a reference datadistribution of output from the sensor group.
 18. A method comprising:acquiring target data serving as an examination target, the target dataoutput by a plurality of sensors; calculating, for each of a pluralityof sensor groups that each include at least two sensors among theplurality of sensors, a degree of outlierness of the target datarelative to a reference data distribution of output from the sensorgroup; and estimating at least one sensor among the plurality of sensorsto be a source of outlierness, based on a comparison of the degrees ofoutlierness of the sensor groups that include the at least one sensor tothe degrees of outlierness of the sensor groups that lack the at leastone sensor.
 19. A computer program product comprising a non-transitorycomputer readable storage medium having program instructions embodiedtherewith, the program instructions executable by a computer to causethe computer to perform operations comprising: acquiring target dataserving as an examination target, the target data output by a pluralityof sensors; calculating, for each of a plurality of sensor groups thateach include at least two sensors among the plurality of sensors, adegree of outlierness of the target data relative to a reference datadistribution of output from the sensor group; and estimating at leastone sensor among the plurality of sensors to be a source of outlierness,based on a comparison of the degrees of outlierness of the sensor groupsthat include the at least one sensor to the degrees of outlierness ofthe sensor groups that lack the at least one sensor.
 20. A computerprogram product comprising a non-transitory computer readable storagemedium having program instructions embodied therewith, the programinstructions executable by a computer to cause the computer to performoperations comprising: acquiring reference data serving as a referencefor output of a plurality of sensors; generating, for each of aplurality of sensor groups that each include at least two sensors amongthe plurality of sensors, a reference data distribution of output fromthe sensor group based on the reference data; and outputting thereference data distribution generated for each of the sensor groups, theoutput reference data distribution to be used to calculate, for each ofthe plurality of sensor groups, a degree of outlierness of target dataserving as an examination target output from the plurality of sensorsrelative to the reference data distribution, and to estimate at leastone sensor among the plurality of sensors to be a source of outlierness,based on a comparison of the degrees of outlierness of the sensor groupsthat include the at least one sensor to the degrees of outlierness ofthe sensor groups that lack the at least one sensor.